# Fight Finance

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The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Net Present Value (NPV) of the project?

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121 If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be: The required return of a project is 10%, given as an effective annual rate. What is the payback period of the project in years? Assume that the cash flows shown in the table are received smoothly over the year. So the$121 at time 2 is actually earned smoothly from t=1 to t=2.

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121 A project has the following cash flows:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 0 2 500

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2. The below graph shows a project's net present value (NPV) against its annual discount rate. For what discount rate or range of discount rates would you accept and commence the project? All answer choices are given as approximations from reading off the graph. You have$100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).

How much can you consume at each time?

An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.

All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).

 Mutually Exclusive Projects Project Costnow ($) Sale price inone year ($) IRR(% pa) Petrol station 9,000,000 11,000,000 22.22 Car wash 800,000 1,100,000 37.50 Car park 70,000 110,000 57.14

Which project should the investor accept?

An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be: • Rented out to a tenant for one year at$0.1m paid immediately, and then sold for $0.99m in one year. • Refurbished into more modern commercial office rooms at a cost of$1m now, and then sold for $2.4m when the refurbishment is finished in one year. • Converted into residential apartments at a cost of$2m now, and then sold for $3.4m when the conversion is finished in one year. All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).  Mutually Exclusive Projects Project Cash flownow ($) Cash flow inone year ($) IRR(% pa) Rent then sell as is -900,000 990,000 10 Refurbishment into modern offices -2,000,000 2,400,000 20 Conversion into residential apartments -3,000,000 3,400,000 13.33 Which project should the investor accept? How many years will it take for an asset's price to double if the price grows by 10% pa? How many years will it take for an asset's price to quadruple (be four times as big, say from$1 to $4) if the price grows by 15% pa? The saying "buy low, sell high" suggests that investors should make a: Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares? A share was bought for$30 (at t=0) and paid its annual dividend of $6 one year later (at t=1). Just after the dividend was paid, the share price fell to$27 (at t=1). What were the total, capital and income returns given as effective annual rates?

The choices are given in the same order:

$r_\text{total}$ , $r_\text{capital}$ , $r_\text{dividend}$.

For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?

Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.

After one year, would you be able to buy , exactly the as or than today with the money in this account?

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.

Inflation is expected to be 2% pa. All rates are given as effective annual rates.

What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.

A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.

Inflation is expected to be 2% pa. All rates are given as effective annual rates.

What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.

Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.

Notes and coins:

How can a nominal cash flow be precisely converted into a real cash flow?

What is the present value of a real payment of $500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa. On his 20th birthday, a man makes a resolution. He will put$30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?

Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.

If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?

An investor bought a bond for $100 (at t=0) and one year later it paid its annual coupon of$1 (at t=1). Just after the coupon was paid, the bond price was $100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate. Which of the following statements is NOT correct? The bond investment produced a: You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt. Which is the safest investment? Which will give the highest returns? Which business structure or structures have the advantage of limited liability for equity investors? Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately. Which of the following statements about book and market equity is NOT correct? The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out. What was CBA's market capitalisation of equity? The investment decision primarily affects which part of a business? The financing decision primarily affects which part of a business? Business people make lots of important decisions. Which of the following is the most important long term decision? The expression 'you have to spend money to make money' relates to which business decision? Katya offers to pay you$10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk. Will you or Katya's deal? This annuity formula $\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)$ is equivalent to which of the following formulas? Note the 3. In the below formulas, $C_t$ is a cash flow at time t. All of the cash flows are equal, but paid at different times. Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you$5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of$1,000 from t=2 to t=7 inclusive.

What is the net present value (NPV) of borrowing from your friend?

Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.

Some countries' interest rates are so low that they're zero.

If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $10 at the end of every year for the next 5 years? In other words, what is the present value of five$10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?

Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this.

Which of the following equations is the 'perpetuity with growth' equation?

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of$1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later$1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of$1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever. Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates. Calculate the current stock price. For a price of$13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa. Would you like to Carla's share or politely ? For a price of$1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa. So the next dividend will be $100(1+0.05)^1=105.00$, and the year after it will be $100(1+0.05)^2=110.25$ and so on. The required return of the stock is 15% pa. Would you like to the share or politely ? The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. $P_0$ is the current share price, $C_1$ is next year's expected dividend, $r$ is the total required return and $g$ is the expected growth rate of the dividend. $$P_0=\dfrac{C_1}{r-g}$$ The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$P_0=\frac{d_1}{r-g}$$ A stock pays dividends annually. It just paid a dividend, but the next dividend ($d_1$) will be paid in one year. According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years? The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0=\dfrac{C_1}{r-g}$$ If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected: A stock will pay you a dividend of$10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be$10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa. What is the stock price today and what do you expect the stock price to be tomorrow, approximately? In the dividend discount model: $$P_0 = \dfrac{C_1}{r-g}$$ The return $r$ is supposed to be the: A stock pays annual dividends which are expected to continue forever. It just paid a dividend of$10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ... After year 4, the annual dividend will grow in perpetuity at 5% pa, so; • the dividend at t=5 will be$1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in three and a half years (t = 3.5)? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0 = \frac{d_1}{r - g}$$ Which expression is NOT equal to the expected dividend yield? A fairly valued share's current price is$4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns. What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain. You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually. • Today is mid-March 2015. • TLS's last interim dividend of$0.15 was one month ago in mid-February 2015.
• TLS's last final dividend of $0.15 was seven months ago in mid-August 2014. Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month. Calculate the current TLS share price. Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts. BigDiv pays large dividends and ZeroDiv doesn't pay any dividends. Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk. Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV. All things remaining equal, which of the following statements is NOT correct? A stock is expected to pay a dividend of$15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates. What is the price of the stock now? Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only: • The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies; • JP Morgan Chase's historical earnings per share (EPS) is$4.37;
• Citi Group's share price is $50.05 and historical EPS is$4.26;
• Wells Fargo's share price is $48.98 and historical EPS is$3.89.

Note: Figures sourced from Google Finance on 24 March 2014.

Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• Apple, Google and Microsoft are comparable companies,
• Apple's (AAPL) share price is $526.24 and historical EPS is$40.32.
• Google's (GOOG) share price is $1,215.65 and historical EPS is$36.23.
• Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71. Source: Google Finance 28 Feb 2014. Details of two different types of light bulbs are given below: • Low-energy light bulbs cost$3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year. • Conventional light bulbs cost only$0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year. The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate. Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order. An industrial chicken farmer grows chickens for their meat. Chickens: 1. Cost$0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
2. Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6). 3. Grow at a rate of$0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
4. Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs$0.30, and so on.
5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).

The required return of the chicken farm is 0.5% given as an effective weekly rate.

Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.

Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.

You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options:

• The private jet can be bought for $6m now, which will cost$12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
• Or the luxury yacht can be bought for $4m now, which will cost$20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.

What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.

Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.

Note that the effective monthly rate is $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$

You're about to buy a car. These are the cash flows of the two different cars that you can buy:

• You can buy an old car for $5,000 now, for which you will have to buy$90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500. • Or you can buy a new car for$14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for$1,000.

Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.

Should you buy the or the ?

Details of two different types of desserts or edible treats are given below:

• High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day. • Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at$4 per day.

The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years. The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate. Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order. Ignore the pain of dental therapy, personal preferences and other factors. A low-quality second-hand car can be bought now for$1,000 and will last for 1 year before it will be scrapped for nothing.

A high-quality second-hand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing. What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate. The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car. An Apple iPhone 6 smart phone can be bought now for$999. An Android Kogan Agora 4G+ smart phone can be bought now for $240. If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost? Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone. Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at$12.95 per week paid in advance on a 2 year contract. After renting the phone, you must return it to Radio-Rentals.

Kogan.com offers the Apple iphone 5S smart phone for sale at $699. You estimate that the phone will last for 3 years before it will break and be worthless. Currently, the effective annual interest rate is 11.351%, the effective monthly interest rate 0.9% and the effective weekly interest rate is 0.207%. Assume that there are exactly 52 weeks per year and 12 months per year. Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order. The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Net Present Value (NPV) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121

For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?

You're considering a business project which costs $11m now and is expected to pay a single cash flow of$11m in one year. So you pay $11m now, then one year later you receive$11m.

Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa. Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct? You have$100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate. You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end. How much can you consume at time zero and one? The answer choices are given in the same order. A project to build a toll road will take 3 years to complete, costing three payments of$50 million, paid at the start of each year (at times 0, 1, and 2).

After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4. The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal. What is the payback period? A firm is considering a business project which costs$10m now and is expected to pay a single cash flow of $12.1m in two years. Assume that the initial$10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?

Which of the following equations is NOT equal to the total return of an asset?

Let $p_0$ be the current price, $p_1$ the expected price in one year and $c_1$ the expected income in one year.

Total cash flows can be broken into income and capital cash flows.

What is the name given to the cash flow generated from selling shares at a higher price than they were bought?

A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).

On which securities must it pay interest or dividend payments in this terrible financial year?

What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?

Let the current share price be $p_0$, the expected future share price be $p_1$, the expected future dividend be $d_1$ and the expected return be $r$. Define the expected return as:

$r=\dfrac{p_1-p_0+d_1}{p_0}$

The answer choices are stated using inequalities. As an example, the first answer choice "(a) $0≤p<∞$ and $0≤r< 1$", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

What was MSFT's market capitalisation of equity?

Which of the following statements is NOT correct?

Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal. Which of the following statements is NOT correct? Which of the following statements about inflation is NOT correct? What is the present value of a nominal payment of$1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the property's expected real total, capital and income returns?

The answer choices below are given in the same order.

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is NOT correct?

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol $\approx$ means 'approximately equal to'.

There are many ways to write the ordinary annuity formula.

Which of the following is NOT equal to the ordinary annuity formula?

The following cash flows are expected:

• 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3). • 1 payment of$400 in 5 years and 6 months (t=5.5) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2. After completion, the toll bridge will yield a constant$50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.

The required return of the project is 21% pa given as an effective annual nominal rate.

All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.

The Net Present Value is:

The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be $C_5$ and the required return be $r$.

So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so $C_5 = C_6 = C_7 = ...$

When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:

A stock just paid its annual dividend of $9. The share price is$60. The required return of the stock is 10% pa as an effective annual rate.

What is the implied growth rate of the dividend per year?

Two years ago Fred bought a house for $300,000. Now it's worth$500,000, based on recent similar sales in the area.

Fred's residential property has an expected total return of 8% pa.

He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments. The present value of 12 months of rental payments is$23,173.86.

The future value of 12 months of rental payments one year ahead is $25,027.77. What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%? The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0 = \frac{d_1}{r-g}$$ Assume that the assumptions of the DDM hold and that the time period is measured in years. Which of the following is equal to the expected dividend in 3 years, $d_3$? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}$$ Which expression is NOT equal to the expected capital return? Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY). • The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies; • ICBC 's historical earnings per share (EPS) is RMB 0.74; • CCB's backward-looking PE ratio is 4.59; • BOC 's backward-looking PE ratio is 4.78; • ABC's backward-looking PE ratio is also 4.78; Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange. Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO). If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy? Assume that: • The medium-sized companies can be bought, merged and sold in an IPO instantaneously. • There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms. • The large merged firm's earnings are the sum of the medium firms' earnings. • The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares. • Return is defined as: $r_{0→1} = (p_1-p_0+c_1)/p_0$ , where time zero is just before the merger and time one is just after. When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever. Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently$1 billion (t=0). The country's GDP is currently $1,000 billion (t=0). In approximately how many years will the company's total dividends be as large as the country's GDP? The following cash flows are expected: • 10 yearly payments of$80, with the first payment in 3 years from now (first payment at t=3).
• 1 payment of $600 in 5 years and 6 months (t=5.5) from now. What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate? A stock’s current price is$1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?

In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.

$$P_0=\dfrac{C_1}{r-g}$$

Which of the following statements about the DDM is NOT correct?

A share’s current price is $60. It’s expected to pay a dividend of$1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM):

$P_0=\dfrac{C_1}{r-g}$

Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.

An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.

The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before $(C_\text{0 before})$.

What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:

A share currently worth $100 is expected to pay a constant dividend of$4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5).

The total required return is 10% pa.

What do you expected the share price to be in 5 years, just after the dividend at that time has been paid?

Which of the following statements is NOT correct? Borrowers:

Which of the following statements is NOT correct? Lenders:

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places.

Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?

A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

$$r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily}$$

Calculate the effective annual rates of the following three APR's:

• A credit card offering an interest rate of 18% pa, compounding monthly.
• A bond offering a yield of 6% pa, compounding semi-annually.
• An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

$r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$

On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity. The bank account pays interest at 6% pa compounding monthly, which is not expected to change. If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment? You want to buy an apartment priced at$300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the$270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).

You want to buy an apartment worth $400,000. You have saved a deposit of$80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$2,000 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change. How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. You just agreed to a 30 year fully amortising mortgage loan with monthly payments of$2,500. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.

You want to buy an apartment priced at $300,000. You have saved a deposit of$30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change. What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month). An 'interest payment' is the same thing as a 'coupon payment'. or ? An 'interest rate' is the same thing as a 'coupon rate'. or ? An 'interest rate' is the same thing as a 'yield'. or ? Calculate the price of a newly issued ten year bond with a face value of$100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid annually. So there's only one coupon per year, paid in arrears every year.

Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months. "Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices. Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to: Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price? A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is$100. What is its price?

Which one of the following bonds is trading at a discount?

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa. A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price. A 10 year bond has a face value of$100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?

Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive.

Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures.

A European company just issued two bonds, a

• 1 year zero coupon bond at a yield of 8% pa, and a
• 2 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 6-month zero coupon bond at a yield of 6% pa, and
• A 12 month zero coupon bond at a yield of 7% pa.

What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 1 year zero coupon bond at a yield of 8% pa, and
• A 2 year zero coupon bond at a yield of 10% pa.

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

You're trying to save enough money to buy your first car which costs $2,500. You can save$100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.

How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.

You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost$2,000, how long will it take for your bank account to reach that amount?

A European company just issued two bonds, a

• 2 year zero coupon bond at a yield of 8% pa, and a
• 3 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

The coupon rate of a fixed annual-coupon bond is constant (always the same).

What can you say about the income return ($r_\text{income}$) of a fixed annual coupon bond? Remember that:

$$r_\text{total} = r_\text{income} + r_\text{capital}$$

$$r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}$$

Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.

Select the most correct statement.

From its date of issue until maturity, the income return of a fixed annual coupon:

A young lady is trying to decide if she should attend university or not.

The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The hard work studying at school in her childhood should be classified as:

Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Sidebar Corp Income Statement for year ending 30th June 2013 $m Sales 405 COGS 100 Depreciation 34 Rent expense 22 Interest expense 39 Taxable Income 210 Taxes at 30% 63 Net income 147  Sidebar Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

Over the next year, the management of an unlevered company plans to:

• Achieve firm free cash flow (FFCF or CFFA) of $1m. • Pay dividends of$1.8m
• Complete a $1.3m share buy-back. • Spend$0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

• All amounts are received and paid at the end of the year so you can ignore the time value of money.
• The firm has sufficient retained profits to pay the dividend and complete the buy back.
• The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Trademark Corp Income Statement for year ending 30th June 2013 $m Sales 100 COGS 25 Operating expense 5 Depreciation 20 Interest expense 20 Income before tax 30 Tax at 30% 9 Net income 21  Trademark Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 120 80 PPE Cost 150 140 Accumul. depr. 60 40 Carrying amount 90 100 Total assets 210 180 Liabilities Current liabilities 75 65 Non-current liabilities 75 55 Owners' equity Retained earnings 10 10 Contributed equity 50 50 Total L and OE 210 180 Note: all figures are given in millions of dollars ($m).

Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 UniBar Corp Income Statement for year ending 30th June 2013 $m Sales 80 COGS 40 Operating expense 15 Depreciation 10 Interest expense 5 Income before tax 10 Tax at 30% 3 Net income 7  UniBar Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 120 90 PPE Cost 360 320 Accumul. depr. 40 30 Carrying amount 320 290 Total assets 440 380 Liabilities Current liabilities 110 60 Non-current liabilities 190 180 Owners' equity Retained earnings 95 95 Contributed equity 45 45 Total L and OE 440 380 Note: all figures are given in millions of dollars ($m).

Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Piano Bar Income Statement for year ending 30th June 2013 $m Sales 310 COGS 185 Operating expense 20 Depreciation 15 Interest expense 10 Income before tax 80 Tax at 30% 24 Net income 56  Piano Bar Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 240 230 PPE Cost 420 400 Accumul. depr. 50 35 Carrying amount 370 365 Total assets 610 595 Liabilities Current liabilities 180 190 Non-current liabilities 290 265 Owners' equity Retained earnings 90 90 Contributed equity 50 50 Total L and OE 610 595 Note: all figures are given in millions of dollars ($m).

Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?

Cash Flow From Assets (CFFA) can be defined as:

Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 World Bar Income Statement for year ending 30th June 2013 $m Sales 300 COGS 150 Operating expense 50 Depreciation 40 Interest expense 10 Taxable income 50 Tax at 30% 15 Net income 35  World Bar Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 200 230 PPE Cost 400 400 Accumul. depr. 75 35 Carrying amount 325 365 Total assets 525 595 Liabilities Current liabilities 150 205 Non-current liabilities 235 250 Owners' equity Retained earnings 100 100 Contributed equity 40 40 Total L and OE 525 595 Note: all figures above and below are given in millions of dollars ($m).

Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Scubar Corp Income Statement for year ending 30th June 2013 $m Sales 200 COGS 60 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 90 Taxes at 30% 27 Net income 63  Scubar Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 60 50 Trade debtors 19 6 Rent paid in advance 3 2 PPE 420 400 Total assets 502 458 Trade creditors 10 8 Bond liabilities 200 190 Contributed equity 130 130 Retained profits 162 130 Total L and OE 502 458 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.

Find the cash flow from assets (CFFA) of the following project.

 Project Data Project life 2 years Initial investment in equipment $8m Depreciation of equipment per year for tax purposes$3m Unit sales per year 10m Sale price per unit $9 Variable cost per unit$4 Fixed costs per year, paid at the end of each year $2m Tax rate 30% Note 1: Due to the project, the firm will have to purchase$40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.

Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch$1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.

Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year. Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?

Your friend just bought a house for $400,000. He financed it using a$320,000 mortgage loan and a deposit of $80,000. In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is$80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So $V=D+E$.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

$$r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0}$$

where $r_{0-1}$ is the return (percentage change) of an asset with price $p_0$ initially, $p_1$ one period later, and paying a cash flow of $c_1$ at time $t=1$.

One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was$70,000 and the other 30,000 was your own wealth or 'equity' in the share assets. The interest rate on the margin loan was 7.84% pa. Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa. What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates. Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E). There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not. Which of the below FFCF formulas include the interest tax shield in the cash flow? $$(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$ $$(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)$$ $$(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c$$ $$(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC$$ $$(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c$$ $$(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC$$ $$(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC$$ $$(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c$$ $$(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC$$ $$(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c$$ The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent. $$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$ $$EBIT=Rev - COGS - FC-Depr$$ $$EBITDA=Rev - COGS - FC$$ $$Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}$$ One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT). \begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\ Does this annual FFCF or the annual interest tax shield? One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT). \begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\ Does this annual FFCF or the annual interest tax shield? A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}}$$ What would you call the expression $C_1/P_0$? You deposit cash into your bank account. Have you or your money? You deposit cash into your bank account. Have you or debt? You deposit cash into your bank account. Does the deposit account represent a debt or to you? You owe money. Are you a or a ? You are owed money. Are you a or a ? You own a debt asset. Are you a or a ? Which of the following statements is NOT correct? Bond investors: A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places. Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct? A European bond paying annual coupons of 6% offers a yield of 10% pa. Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year. All answers are given in the same order: $$r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily}$$ You want to buy an apartment priced at500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the$450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You want to buy an apartment priced at $500,000. You have saved a deposit of$50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage? A prospective home buyer can afford to pay$2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow ($V_\text{before}$), so:

$$\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}}$$

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

Which of the following statements about risk free government bonds is NOT correct?

Hint: Total return can be broken into income and capital returns as follows:

\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned}

The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.

A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price? A firm wishes to raise$10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat. How many bonds should the firm issue? Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?

A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000. Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price? A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away. What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working? The opportunity to meet a desirable future spouse should be classified as: A man is thinking about taking a day off from his casual painting job to relax. He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work. But he's thinking about the hours that he could work today (in the future) which are: A man has taken a day off from his casual painting job to relax. It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now: Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Candys Corp Income Statement for year ending 30th June 2013$m Sales 200 COGS 50 Operating expense 10 Depreciation 20 Interest expense 10 Income before tax 110 Tax at 30% 33 Net income 77
 Candys Corp Balance Sheet as at 30th June 2013 2012 $m$m Assets Current assets 220 180 PPE Cost 300 340 Accumul. depr. 60 40 Carrying amount 240 300 Total assets 460 480 Liabilities Current liabilities 175 190 Non-current liabilities 135 130 Owners' equity Retained earnings 50 60 Contributed equity 100 100 Total L and OE 460 480

Note: all figures are given in millions of dollars ($m). Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Ching-A-Lings Corp Income Statement for year ending 30th June 2013$m Sales 100 COGS 20 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 30 Taxes at 30% 9 Net income 21
 Ching-A-Lings Corp Balance Sheet as at 30th June 2013 2012 $m$m Inventory 49 38 Trade debtors 14 2 Rent paid in advance 5 5 PPE 400 400 Total assets 468 445 Trade creditors 4 10 Bond liabilities 200 190 Contributed equity 145 145 Retained profits 119 100 Total L and OE 468 445

Note: All figures are given in millions of dollars ($m). The cash flow from assets was: Find the cash flow from assets (CFFA) of the following project.  One Year Mining Project Data Project life 1 year Initial investment in building mine and equipment$9m Depreciation of mine and equipment over the year $8m Kilograms of gold mined at end of year 1,000 Sale price per kilogram$0.05m Variable cost per kilogram $0.03m Before-tax cost of closing mine at end of year$4m Tax rate 30%

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year. Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of$3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch$2.5m when it is sold.

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one. Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).  Data on a Levered Firm with Perpetual Cash Flows Item abbreviation Value Item full name $\text{CFFA}_\text{U}$$100m Cash flow from assets excluding interest tax shields (unlevered) $\text{CFFA}_\text{L}$ $112m Cash flow from assets including interest tax shields (levered) $g$ 0% pa Growth rate of cash flow from assets, levered and unlevered $\text{WACC}_\text{BeforeTax}$ 7% pa Weighted average cost of capital before tax $\text{WACC}_\text{AfterTax}$ 6.25% pa Weighted average cost of capital after tax $r_\text{D}$ 5% pa Cost of debt $r_\text{EL}$ 9% pa Cost of levered equity $D/V_L$ 50% pa Debt to assets ratio, where the asset value includes tax shields $t_c$ 30% Corporate tax rate What is the value of the levered firm including interest tax shields? Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ? Your friend just bought a house for$1,000,000. He financed it using a $900,000 mortgage loan and a deposit of$100,000.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000. If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth? Assume that: • No income (rent) was received from the house during the short time over which house prices fell. • Your friend will not declare bankruptcy, he will always pay off his debts. Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations: $$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$ $$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$ What is the formula for calculating annual interest expense (IntExp) which is used in the equations above? Select one of the following answers. Note that D is the value of debt which is constant through time, and $r_D$ is the cost of debt. A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio? Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).  Data on a Levered Firm with Perpetual Cash Flows Item abbreviation Value Item full name $\text{CFFA}_\text{U}$$48.5m Cash flow from assets excluding interest tax shields (unlevered) $\text{CFFA}_\text{L}$ 50m Cash flow from assets including interest tax shields (levered) $g$ 0% pa Growth rate of cash flow from assets, levered and unlevered $\text{WACC}_\text{BeforeTax}$ 10% pa Weighted average cost of capital before tax $\text{WACC}_\text{AfterTax}$ 9.7% pa Weighted average cost of capital after tax $r_\text{D}$ 5% pa Cost of debt $r_\text{EL}$ 11.25% pa Cost of levered equity $D/V_L$ 20% pa Debt to assets ratio, where the asset value includes tax shields $t_c$ 30% Corporate tax rate What is the value of the levered firm including interest tax shields? A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing. Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system. Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer. A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following: \begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned} Does this annual FFCF or the annual interest tax shield? A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed. In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system. You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct? Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's: Taking inflation into account when using the DDM can be hard. Which of the following formulas will NOT give a company's current stock price $(P_0)$? Assume that the annual dividend was just paid $(C_0)$, and the next dividend will be paid in one year $(C_1)$. A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? For an asset's price to quintuple every 5 years, what must be its effective annual capital return? Note that a stock's price quintuples when it increases from say1 to $5. How many years will it take for an asset's price to triple (increase from say$1 to $3) if it grows by 5% pa? If someone says "my shares rose by 10% last year", what do you assume that they mean? A stock is expected to pay a dividend of$1 in one year. Its future annual dividends are expected to grow by 10% pa. So the first dividend of $1 is in one year, and the year after that the dividend will be$1.1 (=1*(1+0.1)^1), and a year later $1.21 (=1*(1+0.1)^2) and so on forever. Its required total return is 30% pa. The total required return and growth rate of dividends are given as effective annual rates. The stock is fairly priced. Calculate the pay back period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year. A share will pay its next dividend of $C_1$ in one year, and will continue to pay a dividend every year after that forever, growing at a rate of $g$. So the next dividend will be $C_2=C_1 (1+g)^1$, then $C_3=C_2 (1+g)^1$, and so on forever. The current price of the share is $P_0$ and its required return is $r$ Which of the following is NOT equal to the expected share price in 2 years $(P_2)$ just after the dividend at that time $(C_2)$ has been paid? A stock will pay you a dividend of$2 tonight if you buy it today.

Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be$2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa. What is the stock price today and what do you expect the stock price to be tomorrow, approximately? A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000. What type of valuation method is the real estate agent using? Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue. Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue. Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm. Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15. Telsa Motors advertises that its Model S electric car saves$570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now. The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings? All other things remaining equal, a project is worse if its: The following cash flows are expected: • A perpetuity of yearly payments of$30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
• One payment of $100 in 6 years and 3 months (t=6.25). What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate? How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay$2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

$$\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1$$

A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of$100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 3 years and have a face value of$100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 10 years and have a face value of$100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years. Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into. Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant. Five years ago you entered into a fully amortising home loan with a principal of$500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 3% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

Five years ago ($t=-5$ years) you entered into an interest-only home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years. Then interest rates suddenly fall to 3% pa ($t=0$), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into. Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant. The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a: • 'Bring Your Own' (BYO) mobile service plan, costing$80 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $100 per month. This plan includes the latest smart phone. Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate. The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs$600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?

A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten$20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then$21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.

A 4.5% fixed coupon Australian Government bond was issued at par in mid-April 2009. Coupons are paid semi-annually in arrears in mid-April and mid-October each year. The face value is $1,000. The bond will mature in mid-April 2020, so the bond had an original tenor of 11 years. Today is mid-September 2015 and similar bonds now yield 1.9% pa. What is the bond's new price? Note: there are 10 semi-annual coupon payments remaining from now (mid-September 2015) until maturity (mid-April 2020); both yields are given as APR's compounding semi-annually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well. An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is$100.

Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

 Project Data Project life 1 year Initial investment in equipment $6m Depreciation of equipment per year$6m Expected sale price of equipment at end of project 0 Unit sales per year 9m Sale price per unit $8 Variable cost per unit$6 Fixed costs per year, paid at the end of each year $1m Interest expense in first year (at t=1)$0.53m Tax rate 30% Government treasury bond yield 5% Bank loan debt yield 6% Market portfolio return 10% Covariance of levered equity returns with market 0.08 Variance of market portfolio returns 0.16 Firm's and project's debt-to-assets ratio 50%

Notes

1. Due to the project, current assets will increase by $5m now (t=0) and fall by$5m at the end (t=1). Current liabilities will not be affected.

Assumptions

• The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
• Millions are represented by 'm'.
• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 2% pa.
• All rates are given as effective annual rates.
• The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

What is the net present value (NPV) of the project?

Which of the following statements about standard statistical mathematics notation is NOT correct?

Diversification in a portfolio of two assets works best when the correlation between their returns is:

All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:

Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.

If the variance of stock A increases but the:

• Prices and expected returns of each stock stays the same,
• Variance of stock B's returns stays the same,
• Correlation of returns between the stocks stays the same.

Which of the following statements is NOT correct?

All things remaining equal, the higher the correlation of returns between two stocks:

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.

• Stock A has an expected return of 5% pa.
• Stock B has an expected return of 10% pa.

What portfolio weights should the investor have in stocks A and B respectively?

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.

• Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
• Stock B has an expected return of 15% pa and a standard deviation of 30% pa.

The correlation coefficient between stock A and B's expected returns is 70%.

What will be the annual standard deviation of the portfolio with this 12% pa target return?

What is the correlation of a variable X with itself?

The corr(X, X) or $\rho_{X,X}$ equals:

What is the correlation of a variable X with a constant C?

The corr(X, C) or $\rho_{X,C}$ equals:

Three important classes of investable risky assets are:

• Corporate debt which has low total risk,
• Real estate which has medium total risk,
• Equity which has high total risk.

Assume that the correlation between total returns on:

• Corporate debt and real estate is 0.1,
• Corporate debt and equity is 0.1,
• Real estate and equity is 0.5.

You are considering investing all of your wealth in one or more of these asset classes. Which portfolio will give the lowest total risk? You are restricted from shorting any of these assets. Disregard returns and the risk-return trade-off, pretend that you are only concerned with minimising risk.

A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?

Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?

A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?

Assets A, B, M and $r_f$ are shown on the graphs above. Asset M is the market portfolio and $r_f$ is the risk free yield on government bonds. Which of the below statements is NOT correct?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

What do you think will be the stock's expected return over the next year, given as an effective annual rate?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last year, given as an effective annual rate?

The CAPM can be used to find a business's expected opportunity cost of capital:

$$r_i=r_f+β_i (r_m-r_f)$$

What should be used as the risk free rate $r_f$?

A firm's WACC before tax would decrease due to:

In the dividend discount model:

$$P_0= \frac{d_1}{r-g}$$

The pronumeral $g$ is supposed to be the:

Which of the following is NOT a synonym of 'required return'?

Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?

According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?

The security market line (SML) shows the relationship between beta and expected return.

Investment projects that plot on the SML would have:

Examine the following graph which shows stocks' betas $(\beta)$ and expected returns $(\mu)$:

Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Which of the following statements is NOT correct?

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose$256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose$256. Which of the following statements is NOT correct?

Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:

Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.

This is much higher than the previous forecast of 3% pa.

A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.

What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:

• Inflation remains at 5% over the next 2 years.
• Investors demand a constant real bond yield.
• The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.

The efficient markets hypothesis (EMH) and no-arbitrage pricing theory is most closely related to which of the following concepts?

The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were$80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below:

Taxable income Tax on this income
0 – $18,200 Nil$18,201 – $37,000 19c for each$1 over $18,200$37,001 – $80,000$3,572 plus 32.5c for each $1 over$37,000
$80,001 –$180,000 $17,547 plus 37c for each$1 over $80,000$180,001 and over $54,547 plus 45c for each$1 over $180,000 The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations How much personal income tax would you have to pay per year if you earned$80,204.80 per annum before-tax?

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner. The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%. The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes. What will be the personal tax payable by the shareholder and the corporate tax payable by the company? Which of the following statements about Australian franking credits is NOT correct? Franking credits: A small private company has a single shareholder. This year the firm earned a$100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

A mining firm has just discovered a new mine. So far the news has been kept a secret.

The net present value of digging the mine and selling the minerals is $250 million, but$500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment. The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after. Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets $(\Delta V)$, market capitalisation of debt $(\Delta D)$ and market cap of equity $(\Delta E)$? Assume that markets are semi-strong form efficient. The triangle symbol $\Delta$ is the Greek letter capital delta which means change or increase in mathematics. Ignore the benefit of interest tax shields from having more debt. Remember: $\Delta V = \Delta D+ \Delta E$ In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events: • 23/10/2003. Share price closes at$18.30.

• 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens. • 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at$18.00 and closes at \$18.14.

All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

Convert a 10% continuously compounded annual rate $(r_\text{cc annual})$ into an effective annual rate $(r_\text{eff annual})$. The equivalent effective annual rate is:

Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.

A continuously compounded monthly return of 1% $(r_\text{cc monthly})$ is equivalent to a continuously compounded annual return $(r_\text{cc annual})$ of:

An effective monthly return of 1% $(r_\text{eff monthly})$ is equivalent to an effective annual return $(r_\text{eff annual})$ of:

Which of the following quantities is commonly assumed to be normally distributed?

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.

Which of the below statements is NOT correct?

If a stock's future expected effective annual returns are log-normally distributed, what will be bigger, the stock's or effective annual return? Or would you expect them to be ?

The symbol $\text{GDR}_{0\rightarrow 1}$ represents a stock's gross discrete return per annum over the first year. $\text{GDR}_{0\rightarrow 1} = P_1/P_0$. The subscript indicates the time period that the return is mentioned over. So for example, $\text{AAGDR}_{1 \rightarrow 3}$ is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:

$$r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)$$

He then took the arithmetic average and found it to be 1% per month using this formula:

$$\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}$$

He also found the standard deviation of these monthly returns which was 5% per month:

$$\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}$$

Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.